For practical purposes, there are plenty of tetrahedral partitions that satisfy our definition in Section 2.1, wherein the Delaunay tetrahedral partition is most preferred. The Delaunay tetrahedral partition has been well-studied with superior properties for 2D objects [1]}, [2]}, for example, a 2D Delaunay triangulation is “angle optimal", i.e., it maximizes the minimum angle in a triangulation. Extending the 2D Delaunay triangulation to higher dimensionality, a 3D Delaunay tetrahedral partition possesses similar property that it maximizes the minimal solid angle in the tetrahedra.
